x | y
-------
1 | 65
2 | 105
3 | 145
HELP!!!​

Answer:

(2x+3y)^2

= (2x)^2 + 2(2x)(3y) + (3y)^2

= 4x^2 + 12xy + 9y^2

Answer:

4x^2 12xy +9y^2

Step-by-step explanation:

(2x+3y)^2

(2x+3y)(2x+3y)

FOIL

4x^2 + 6xy+6xy + 9y^2

4x^2 12xy +9y^2

Given that F is a continuous function and ∫[0 to 81] f(x) dx = 8, therefore the value of the integral ∫[0 to 9] xf(x²) dx is 4/81.

Let's begin by substituting u = x² into the integral ∫[0 to 9] xf(x²) dx. This substitution allows us to express the integral in terms of u instead of x. To determine the new limits of integration, we substitute the original limits of integration into the equation u = x². When x = 0, u = 0, and when x = 9, u = 9² = 81. Therefore, the new integral becomes ∫[0 to 81] (1/2) f(u) du.

We know that ∫[0 to 81] f(x) dx = 8, which implies that ∫[0 to 81] (1/81) f(x) dx = (1/81) * 8 = 8/81. Now, in the substituted integral, we have (1/2) multiplied by f(u) and du as the differential. To find the value of this integral, we need to evaluate ∫[0 to 81] (1/2) f(u) du.

Since we have the value of ∫[0 to 81] f(x) dx = 8, we can substitute it into the integral to obtain (1/2) * 8/81. Simplifying this expression, we find the value of ∫[0 to 9] xf(x²) dx = 4/81.

Therefore, the value of the integral ∫[0 to 9] xf(x²) dx is 4/81.

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Answer:

ok

Step-by-step explanation:

ok

Answer:

The answer is I don't know

Energy and mass are related by the formula, E = mc², where m is the mass of the object and c is the speed of light. The equation that finds m, given e and c, is:   m = E/c²

The equation, E = mc² was coined from Albert Einstein's theory of relativity, which shows the relationship between mass and energy. It shows that energy and mass can be interchanged into each other. The equation tells us that if we multiply the mass of a body (m) with the square of the speed of light (c²), we will get the total amount of energy (E) contained in that body, which can potentially be converted to other forms of energy.

However, if are given the energy contained in a body and the speed of light, then told to find the mass of the body, we will divide the equation by the coefficient of m. The coefficient of m in the equation is c², thus:

                          E = mc²

                          E/c² = mc²/c²

   c² divided by c² is 1, therefore, the new equation is:

                               m = E/c²

 Thus, the equation that finds m, given e and c is m = E/c².

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Answer:

Step-by-step explanation:

Conversion ratio = 8/5 = 1.6

So,

     25.9 miles = 25.9 x 1.6

                       = 41.44 km

The antiderivative of f(x) = tan(eˣ + π/2) on 0≤x≤ln(π/2) is:

⇒  ln |sec(\(e^{\pi /2}\))| / \(e^{\pi /2}\)

Now, For the antiderivative of f(x) = tan(eˣ + π/2) on the interval 0≤x≤ln(π/2), we need to integrate the given function.

Now, using the substitution u = eˣ + π/2.

Then, we have:

du/dx = eˣ

dx = du / eˣ

Using this substitution, we can rewrite the original function as:

f(x) = tan(eˣ + π/2) dx = tan(u) du / eˣ

Now let's integrate this function:

∫tan(u) du / eˣ = - ln |cosec(u)| / eˣ + C

Substituting back u = eˣ+π/2:

ln |cosec(eˣ + π/2)| / eˣ + C

= - ln |cosec(eˣ + π/2)| / eˣ + C

Now we need to evaluate this expression at the limits of integration x = 0 and x = ln(π/2):

F(ln(π/2)) - F(0)

= - ln |cosec(\(e^{\pi /2 } + \frac{\pi }{2}\))| / \(e^{\pi /2}\) + C - (- ln |cos(0)| / \(e^{\pi /2}\) + C)

= - ln |sec(\(e^{\pi /2}\))| / \(e^{\pi /2}\) + ln |cos(0)| / \(e^{\pi /2}\)

= - ln |sec(\(e^{\pi /2}\))| / \(e^{\pi /2}\) + ln(1) / \(e^{\pi /2}\)

=  ln |sec(\(e^{\pi /2}\))| / \(e^{\pi /2}\)

So, the antiderivative of f(x) = tan(eˣ + π/2) on 0≤x≤ln(π/2) is:

⇒  ln |sec(\(e^{\pi /2}\))| / \(e^{\pi /2}\)

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Answer:

The probability of choosing a heart, P(Heart) = 13/52 = 0.25

Step-by-step explanation:

Answer: Two sets are disjoint if they have no elements in common.

(i) The first set is {1, 2, 3, 4} and the second set is {x : x is a natural number and 4 ≤ x ≤ 6}. The second set contains the numbers 4, 5, and 6. The first set contains the number 4. Therefore, the two sets have one element in common, which means they are not disjoint.

(ii) The first set is {a, e, i, o, u} and the second set is {c, d, e, f}. The two sets have the letter "e" in common, but no other elements in common. Therefore, they are not disjoint.

(iii) The first set is {x : x is an even integer} and the second set is {x : x is an odd integer}. Even and odd integers have different parity, so they have no elements in common. Therefore, these two sets are disjoint.

In summary, the only pair of sets that are disjoint is the set of even integers and the set of odd integers.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

trust me on this one

The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

Answer:

28 g. ................

Answer:

Step-by-step explanation:

Find area and perimeter of square of side 5cm

P = 4 × side

A = l x l

Perimeter

5 * 4 = 20 cm

Area

5 * 5 = 25 cm²

The logistic population growth model, dN/dt = rN (K N/K), describes a populations growth when an upper growth is assumed.This upper limit to growth is known as the carrying capacity (K), and as the population size (N) gets larger, (dN/dt) decreases.

The carrying capacity represents the maximum number of individuals that the environment can sustainably support with available resources and space.

It is the point at which the population's growth rate slows down and eventually reaches equilibrium.

As the population size (N) gets larger, the rate of change of population (dN/dt) decreases. This means that the population growth rate slows down as it approaches the carrying capacity.

When the population size is significantly smaller than the carrying capacity, the growth rate is relatively high as there are abundant resources available.

However, as the population size approaches the carrying capacity, resources become limited, competition increases, and factors like food availability, space, and environmental constraints start to exert a greater influence on population growth.

Eventually, as the population size reaches or nears the carrying capacity, the growth rate approaches zero, resulting in a stable population size.

This is because the population is in balance with the available resources, and the birth rate is approximately equal to the death rate.

At this point, the population maintains a relatively stable size over time, fluctuating around the carrying capacity in response to changes in environmental conditions or other factors.

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Answer:

48

Step-by-step explanation:

since this is a linear Angle, the total sum will be 180. Given Angle is 132. so answer will be:

180-132= 48

Answer:

Step-by-step explanation:

The sum of adjacent angles on a straight line is 180°. i.e. In the figure, we are given is a straight line, then n and 132° are the adjacent angles.

n + 132° = 180

n = 180 - 132

n = 48

Hence, the measure of the unknown angle is 48°.

The geometric term best describes Marci's description of the sun's light is ray

A ray is a line that extends eternally in one direction from a point in geometry, in this case the sun.

It symbolizes a straight journey without any turning points.

As the sun's light propagates in a straight line throughout space without end, Marci's description fits the definition of a ray.

To explain Marci's depiction of the sun's light as a line that originates at the sun and never ends is to use the geometric term "ray."

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Answer: Ray

Step-by-step explanation:

A ray continues but may have a segment near the stopping point

Answer:

No

Step-by-step explanation:

4 x 2 = 14

BUT

3 x 2 ≠ 9

they are not equal because if is simplify 3/7 you will not get 9/14 you will get 6/14

like this

3|7

6|14

Answer:

3πx³ + 20πx² + 44πx + 32π

Step-by-step explanation:

Volume of a cylinder = πr²h

Where,

r = radius of the cylinder

h = height of the cylinder

r = x+2

h = 3x + 8

Volume of a cylinder = πr²h

= π × (x+2)² × 3x + 8

= (3xπ + 8π) × (x + 2)²

= (3πx + 8π) + (x² + 4x + 4)

= 3πx³ + 12πx² + 12πx + 8πx² + 32πx + 32π

= 3πx³ + 20πx² + 44πx + 32π

Note:

(x + 2)²

= (x + 2) (x + 2)

= x² + 2x + 2x + 4

= x² + 4x + 4

Answer:

\(f(n) = \frac{32}{3}(\frac{3}{2})^n\)

Step-by-step explanation:

Given

\(r = \frac{3}{2}\)

\(f(5) = 81\)

Required

The geometric sequence

A geometric sequence is represented as:

\(f(n) = ar^{n-1}\)

Replace n with 5

\(f(5) = ar^{5-1}\)

\(f(5) = ar^4\)

Substitute values for f(5) and r

\(81 = a* (\frac{3}{2})^4\)

Open bracket

\(81 = a* \frac{81}{16}\)

Make a the subject

\(a = \frac{81 * 16}{81}\)

\(a = 16\)

So, the explicit function is:

\(f(n) = ar^{n-1}\)

\(f(n) = 16 * (\frac{3}{2})^{n-1}\)

Split

\(f(n) = 16 * (\frac{3}{2})^n \div (\frac{3}{2})\)

Convert to multiplication

\(f(n) = 16 * (\frac{3}{2})^n * \frac{2}{3}\)

\(f(n) = \frac{32}{3}(\frac{3}{2})^n\)

Answer:

f(x) = 16*(3/2)^(x-1)

Step-by-step explanation:

right on edge

To test the hypothesis H₁: μx = μy versus Hoxy, where μx and μy represent the means of X and Y respectively, we can perform a two-sample t-test. The test compares the means of two independent samples to determine if they are significantly different from each other.

The given information provides the sample means (X = 33.8, Y = 32.5) and the sample standard deviations (Sx = 3.9, Sy = 5.1). The sample sizes for both X and Y are n = m = 25.

Using this information, we can calculate the test statistic, which is given by:

t = (X - Y) / sqrt((Sx^2 / n) + (Sy^2 / m))

Plugging in the values, we get:

t = (33.8 - 32.5) / sqrt((3.9^2 / 25) + (5.1^2 / 25))

Next, we need to determine the degrees of freedom for the t-distribution. Since the sample sizes are equal (n = m = 25), the degrees of freedom for the test is given by (n + m - 2).

Using the t-distribution table or software, we can find the critical value corresponding to a significance level of α = 0.05 and the degrees of freedom.

Finally, we compare the calculated test statistic with the critical value. If the test statistic falls within the rejection region (i.e., the absolute value of the test statistic is greater than the critical value), we reject the null hypothesis. The p-value can also be calculated, which represents the probability of observing a test statistic as extreme or more extreme than the calculated value, assuming the null hypothesis is true.

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Given the coordinates above, the area of the trapezoid is approximately 41. See the explanation below.

A trapezoid is a quadrilateral with at least one set of parallel sides in American and Canadian English. A trapezoid is known as a trapezium in British and other varieties of English.

For the calculation showing the above solution:

Step 1 - Given:

A = (-3,2)

B = (1, 5)  = ⊥

C = (-7, -3)

D = (0.-2)

Step 2 - To get the distance between the points we need to use the formula for Distance between two points which is given as:

d=√((x2 – x1)² + (y2 – y1)²).

Distance of Line AB =

√((1 – (-3))² + (5 – 2)²).

= √[(4)² + (3)²]

= √( 16 + 9)
= √25

AB= 5

Repeat this for  BC, CD, DA and we'd get the following

BC =  11.313708498985
CD = 7.0710678118655

DA = 5

Step 3  - From the above structure, [see attached] we then apply the formula for the area of a Trapezoid (Trapezium) which is given as:

A = [(a+b)/2] h

Where a = 5

b = 11.313708498985

h = 5

=  [(5+11.313708498985)/2] 5

= 40.7842712475

\(\approx\) 41

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Proofreading refers to the checking for errors in a text before it is published or shared. It is the last stage of the writing process. One correct minor spelling and punctuation mistakes.

The following are the symbols in proofreading;

lc - lowercase a letter

bf - set in boldface

ital - set in italics

sp - spell out

cap - change from lowercase to uppercase/ capital letter

here, we have,

lc

so, we get,

Therefore, the correct answer is option C. Lowercase a letter.

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6. The probability that all 5 couples will have a baby of the preferred gender is 0.2373.

7. The probability that at least 4 of the 5 couples will have a baby of the preferred gender is 1 - 0.3672 = 0.6328.

Probability is a way to gauge how likely something is to happen. Many things are difficult to predict with absolute certainty.

Answer: The probability that one couple will have a baby of the preferred gender is 0.75. Assuming the gender of each baby is independent of the others, the probability that all 5 couples will have a baby of the preferred gender is 0.75⁵ = 0.2373.

Numeric value: 0.2373

In words: The probability that all 5 couples will have a baby of the preferred gender is 0.2373.

Answer: There are two ways to approach this problem. One way is to calculate the probability of each possible outcome (0 to 5 couples having a baby of the preferred gender) and then add up the probabilities for the outcomes where at least 4 couples have a baby of the preferred gender. Another way is to use the complement rule and subtract the probability that fewer than 4 couples have a baby of the preferred gender from 1.

Using the first method, we can calculate the probabilities as follows:

- 0 couples: 0.25⁵ = 0.0009766

- 1 couple: 5 x 0.75 x 0.25⁴ = 0.01465

- 2 couples: 10 x 0.75² x 0.25³ = 0.08789

- 3 couples: 10 x 0.75³ x 0.25² = 0.2637

- 4 couples: 5 x 0.75⁴ x 0.25 = 0.3955

- 5 couples: 0.75⁵ = 0.2373

The probabilities for the outcomes where at least 4 couples have a baby of the preferred gender are 0.3955 and 0.2373, so the total probability is 0.3955 + 0.2373 = 0.6328.

Using the second method, we can calculate the probability that fewer than 4 couples have a baby of the preferred gender as follows:

- 0 couples: 0.25⁵ = 0.0009766

- 1 couple: 5 x 0.75 x 0.25⁴ = 0.01465

- 2 couples: 10 x 0.75² x 0.25³ = 0.08789

- 3 couples: 10 x 0.75³ x 0.25² = 0.2637

The probability that fewer than 4 couples have a baby of the preferred gender is the sum of these probabilities: 0.0009766 + 0.01465 + 0.08789 + 0.2637 = 0.3672.

Therefore, the probability that at least 4 of the 5 couples will have a baby of the preferred gender is 1 - 0.3672 = 0.6328.

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It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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The coordinates of a point are stated in the order, abscissa (x coordinate) first, then comes the ordinate (y coordinate)

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

\(=2*\sqrt{8(4)} +\frac{4}{3}\\ =2*\sqrt{32} +\frac{4}{3}\\=2*\sqrt{16*2} +\frac{4}{3}\\=2*\sqrt{16} *\sqrt{2} +\frac{4}{3}\\=2*4\sqrt{2} +\frac{4}{3} \\=8\sqrt{2} +\frac{4}{3}\\ =12.64704183\\\)

⇒Note it is up to you to HOW MANY DECIMAL PLACES YOU ROUND TO.

Answer:

  (d)  30 units²

Step-by-step explanation:

The area of the rectangle is the product of the length and width. It is equal to the number of unit squares that fill the rectangle.

__

By counting grid squares or subtracting coordinates, we can see this rectangle is 3 units wide and 10 units high. Its area will be ...

  A = WH

  A = (3 units)(10 units) = 30 units²

_____

Additional comment

You can also count the three columns of 10 shaded squares, or the 10 rows of 3 shaded squares. Either way, you will count 30 square units covering the rectangle.